Is homework worth the time?

I have never been sure whether I should be assigning homework in my classes. For one, they give additional work, from their formulation to their grading. Second, I am not sure of their effectiveness, in particular given that the students doing them are the ones that least need them. The same applies to extra credit problems. But before college, homeworks are routinely given to children who mostly have no choice but hand them in. Are homeworks worth the time spent on them? While my children certainly spend spend less time on them than I did at the same age (it only appears they spend more time, they are constantly distracted, see yesterday's rant on the Internet at the workplace...), do they really learn with them?

Ozkan Eren and Daniel Henderson use the National Educational Longitudinal Study to not only look at achievement in mathematics, as previous studies, but also in science, English and history. And it is only in mathematics that homework matters (positively). I am especially astonished that homework does not matter in English, as practice certainly improves ones writing (and I should obviously have done more homework). But my impression appears to be wrong.